BV-Regularity of the Boltzmann Equation in Non-Convex Domains

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In: Archive for Rational Mechanics and Analysis, 220(2016), 3, S. 1045 - 1093
Format: E-Article
Sprache: Englisch
veröffentlicht: Springer Berlin Heidelberg
Schlagworte:
ISSN: 0003-9527
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finc.format ElectronicArticle
finc.mega_collection Springer Journals
finc.id dswarm-105-MTAuMTAwNy9zMDAyMDUtMDE1LTA5NDgtOQ
finc.record_id 10.1007/s00205-015-0948-9
finc.source_id 105
ris.type EJOUR
rft.atitle BV-Regularity of the Boltzmann Equation in Non-Convex Domains
rft.eissn 1432-0673
rft.epage 1093
rft.genre article
rft.issn 0003-9527
rft.issue 3
rft.jtitle Archive for Rational Mechanics and Analysis
rft.pages 1045-1093
rft.place Berlin/Heidelberg
rft.pub Springer Berlin Heidelberg
rft.date 2016
x.date 2016-06-01T00:00:00Z
rft.stitle Arch Rational Mech Anal
rft.spage 1045
rft.volume 220
abstract We consider the Boltzmann equation in a general non-convex domain with the diffuse boundary condition. We establish optimal BV estimates for such solutions. Our method consists of a new <Emphasis Type="Italic">W</Emphasis><Superscript>1,1</Superscript>-trace estimate for the diffuse boundary condition and a delicate construction of an <InlineEquation ID="IEq1"><InlineMediaObject><ImageObject Type="Linedraw" Rendition="HTML" Format="GIF" FileRef="205_2015_948_Article_IEq1.gif" Color="BlackWhite"/></InlineMediaObject><EquationSource Format="TEX">$${\varepsilon}$$</EquationSource><EquationSource Format="MATHML"><math xmlns:xlink="http://www.w3.org/1999/xlink"><mi mathvariant="italic" xmlns:xlink="http://www.w3.org/1999/xlink">ε</mi></math></EquationSource></InlineEquation>-tubular neighborhood of the singular set.
authors Guo Y.
doi 10.1007/s00205-015-0948-9
languages eng
url https://doi.org/10.1007/s00205-015-0948-9
x.subjects Boltzmann Equation
Radon Measure
Trace Theorem
Duhamel Formula
Diffuse Boundary Condition